Example 56.7 FCS Method for CLASS Variables

This example uses FCS methods to impute missing values in both continuous and CLASS variables in a data set with an arbitrary missing pattern. The following statements invoke the MI procedure and impute missing values for the Fish3 data set:

The DISCRIM option uses the discriminant function method to impute the classification variable Species, and the REG option uses the regression method to impute the continuous variable Height. By default, the regression method is also used to impute other continuous variables, Length and Width.

The "Model Information" table in Output 56.7.1 describes the method and options used in the multiple imputation process.

Output 56.7.1
Model Information

The MI Procedure

Model Information

Data Set

WORK.FISH3

Method

FCS

Number of Imputations

5

Number of Burn-in Iterations

5

Seed for random number generator

1305417

The "FCS Model Specification" table in Output 56.7.2 describes methods and imputed variables in the imputation model. The procedure uses the discriminant function method to impute the variable Species, and the regression method to impute other variables.

Output 56.7.2
FCS Model Specification

FCS Model Specification

Method

Imputed Variables

Regression

Length Height Width

Discriminant Function

Species

The "Missing Data Patterns" table in Output 56.7.3 lists distinct missing data patterns with corresponding frequencies and percentages. With the default ORDER=FREQ option, the variable ordering by the descending frequency counts is used for the missing values in the filled-in and imputation phases.

Output 56.7.3
Missing Data Patterns

Missing Data Patterns

Group

Length

Height

Width

Species

Freq

Percent

Group Means

Length

Height

Width

1

X

X

X

X

38

73.08

41.515789

12.531526

5.266474

2

X

X

X

.

3

5.77

38.433333

11.797667

4.587667

3

X

X

.

.

3

5.77

45.033333

13.647667

.

4

X

.

X

.

2

3.85

36.100000

.

5.135000

5

X

.

.

.

2

3.85

40.150000

.

.

6

.

X

X

X

2

3.85

.

14.448000

6.886000

7

.

X

.

X

1

1.92

.

18.037000

.

8

.

X

.

.

1

1.92

.

12.444000

.

With the specified DETAILS option for variables Species and Height, parameters used in each imputation for these two variables are displayed in the "Group Means for FCS Discriminant Method" table in Output 56.7.4 and in the "Regression Models for FCS Method" table in Output 56.7.5.

Output 56.7.4
FCS Discrim Model for Species

Group Means for FCS Discriminant Method

Species

Variable

Imputation

1

2

3

4

5

Bream

Length

-0.020460

-0.375046

-0.455147

-0.227513

-0.149084

Bream

Height

0.693833

0.623187

0.744749

0.580846

0.714942

Bream

Width

0.397506

0.173774

0.421867

0.167947

0.300103

Pike

Length

0.845745

1.304043

0.708257

1.063104

0.382590

Pike

Height

-1.357333

-1.140244

-1.367343

-1.269584

-1.342550

Pike

Width

-0.341246

0.193092

-0.517978

-0.366050

-0.438790

Output 56.7.5
FCS Regression Model for Height

Regression Models for FCS Method

ImputedVariable

Effect

Species

Imputation

1

2

3

4

5

Height

Intercept

-0.341941

-0.366473

-0.315587

-0.361090

-0.324455

Height

Length

0.119780

0.126889

0.011333

0.137968

0.117460

Height

Width

0.350410

0.310695

0.441925

0.345254

0.317621

Height

Species

Bream

0.987346

1.008808

0.851794

0.999192

0.999200

The following statements list the first 10 observations of the data set outex7 in Output 56.7.6:

After the completion of five imputations by default, the "Variance Information" table in Output 56.7.7 displays the between-imputation variance, within-imputation variance, and total variance for combining complete-data inferences for continuous variables. The relative increase in variance due to missingness, the fraction of missing information, and the relative efficiency for each variable are also displayed. These statistics are described in the section Combining Inferences from Multiply Imputed Data Sets.

Output 56.7.7
Variance Information

Variance Information

Variable

Variance

DF

RelativeIncreasein Variance

FractionMissingInformation

RelativeEfficiency

Between

Within

Total

Length

0.158766

1.287899

1.478418

36.33

0.147930

0.136011

0.973518

Height

0.007807

0.310949

0.320317

47.194

0.030127

0.029661

0.994103

Width

0.002160

0.016085

0.018677

35.138

0.161157

0.146966

0.971446

The "Parameter Estimates" table in Output 56.7.8 displays a 95% mean confidence interval and a t statistic with its associated p-value for each of the hypotheses requested with the default MU0=0 option.